Population Mean Waiting Time

a) You are the manager of a fast food restaurant. You want to determine whether the population meanwaiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. From past experience, you can assume that the population is normally distributed with a population standard deviationof 1.5 minutes. You select a sample of 25 orders during a one hour period. The sample mean is 5.2 minutes. Determine whether there is evidence at the 0.05 level of significance that the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes.

b. You have just opened your new fast-food restaurant. And you have developed a new process to ensure that orders at the drive-through are filled correctly. The previous process filled orders correctly 85% of the time. Based on a sample of a hundred orders using the new process, 95 were filled correctly. At the 0.01 level of significance, can you conclude that the new process has increased the proportion of orders filled correctly?

Please see the attachments for full solutions.

a)
The null hypothesis tested is
H0: Mean waiting time to place an order = 4.5. (µ = 4.5)
The alternative hypothesis is
H1: Mean waiting time to place an order ? 4.5. (µ ? 4.5)
The test statistic used is . Given that = 5.2, n = 25, ? = 1.5
Therefore, Z = 2.333333333

Rejection Criteria: Reject the null hypothesis, if the absolute …